Summary: Twistorial constructions of special Riemannian
manifolds
Rui Albuquerque
Departamento de Matemática da Universidade de Évora and Centro de Investigação em
Matemática e Aplicações (CIMA), Rua Romão Ramalho, 59, 7000 Évora, Portugal.
rpa@dmat.uevora.pt
Abstract.
We use twistor theory to describe virtualy new constructions of Hermitian and quaternionic
Kähler structures on tangent bundles and a G2 structure on the unit sphere tangent bundle of a
Riemannian 4-manifold -- fundamental to holonomy theory and subject of deep research in physics.
We interpret "self-holomorphic" complex structures on a symplectic manifold. These complex
structures give an interesting set of problems in the first possible dimension, the case of Riemann
surfaces, from which should follow some interplay with Teichmuller theory, as well as with SL(2)
connections.
Keywords: connections with torsion, Hermitian, quaternionic, Kähler, symplectic, G2 structures.
PACS: 02.40.Ky,02.40.Tt,11.25.Hf,11.25.Mj
Introduction
Twistor theory can be applied in several situations. With M. Berger's classification of
non-symmetric, locally irreducible Riemannian holonomy groups in mind and looking
forward for more recent studies of geometry with torsion, we were lead to the twistorial